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Bezier curves:
Theses are special polynomial curves expressed using Bernstein polynomials. Spline curves are simple extensions of Bézier curves composed of two or more polynomial curves joined in a sequence in such a way that the resulting curve is atleast continuous. Formula to compute points on a Bézier curve P is as follows:
Where {bi} are the control points of the curve and Bni(t) are Bernstein polynomials.
note on control points
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